Pressure at the walls of a container

In summary, the conversation discusses the energy of each molecule in a gas, which is represented by the equation ##\frac{1}{2}mv_{rms}^2 \Rightarrow E/3 = \frac{1}{2}mv_i^2##. The total energy of each type of gas is then calculated using the equation ##E_i = N_i\frac{3}{2}mv_i^2##. The conversation also mentions the relationship between pressure and energy, specifically ##PV=E##. However, it is noted that this equation cannot be used without further information about the x and z components of velocity. Therefore, the final answer is given as ##m \sum_i n_i v_i^2 ##.
  • #1
Kaguro
221
57
Homework Statement
Consider a cube ABCDEFGH of volume V containing N molecules each of mass m with
uniform density n =N/V . Suppose this system is equivalent to a system of M non-interacting gases such that molecules of the i th gas are N_i = n_i*V in number, each with an
identical y -component of velocity v_i . What is the pressure P on the surface , ABCD of
area A, perpendicular to the positive y axis?
Relevant Equations
PV=NkT, where N is total number of molecules
Vrms=sqrt(1.5kT)
I wrote energy of each molecule is ##\frac{1}{2}mv_{rms}^2 \Rightarrow E/3 = \frac{1}{2}mv_i^2##. So total energy of each type of gas is
##E_i = N_i\frac{3}{2}mv_i^2## Now, PV=E. So total Pressure = Sum of energies/volume
##P=\frac{\frac{3m}{2}\sum_i N_i v_i^2}{V} =\frac{3m}{2} \sum_i n_i v_i^2 ##

But answer given is just ##m \sum_i n_i v_i^2 ##
Help.
 
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  • #2
You are not told anything about the x and z components of the velocity. You cannot assume that they are the same as the y component, or that the pressure is isotropic, so you can't use PV = E.
Incidentally, there is presumably a mistake in the question; at any instant half the molecules have y-velocity vi, and the other half -vi.
 

Related to Pressure at the walls of a container

What is pressure at the walls of a container?

Pressure at the walls of a container is the force exerted by the gas molecules inside the container on the walls of the container. It is a measure of how much the gas molecules are colliding with the walls of the container.

How is pressure at the walls of a container measured?

Pressure at the walls of a container is typically measured using a pressure gauge. This device measures the force per unit area exerted by the gas molecules on the walls of the container.

What factors affect pressure at the walls of a container?

The pressure at the walls of a container is affected by the number of gas molecules inside the container, the temperature of the gas, and the volume of the container. An increase in any of these factors will result in an increase in pressure at the walls of the container.

Why is pressure at the walls of a container important?

Pressure at the walls of a container is important because it helps determine the behavior of gases. It is also a crucial factor in many industrial and scientific processes, such as in the design of pressure vessels and in gas laws.

How does pressure at the walls of a container change with altitude?

The pressure at the walls of a container decreases as altitude increases. This is because at higher altitudes, there are fewer gas molecules present, resulting in fewer collisions with the walls of the container and therefore a lower pressure.

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